−0.5 0 0.5
−4
−2 0 2
4 x/Dh = 0.35
W/U0 y/Dh
−0.5 0 0.5 x/Dh = 0.7
W/U0
−0.5 0 0.5 x/Dh= 1.5
W/U0
−0.5 0 0.5 x/Dh = 2.2
W/U0 Isothermal Detached flame V-flame
Figure 9.1: Comparison of the tangential velocity component for the isothermal case, the detached flame, and the V-flame. Operating conditions are provided in Tab. 4.2.
on the phase of the PVC (θ) and on the forcing phase (Ψ)
v(x, t) =V(x) +vc,ha(x, θ(t),Ψ(t)) +vs(x, t). (9.1) The phase with respect to the PVC oscillation (θ) is obtained from a POD analysis using Eqn. 2.38 and the phase with respect to the forcing cycle (Ψ) is extracted from the time traces of the excitation signal. Subsequently, the doubly phase-resolved velocity fluctuations are obtained as
vc,ha(x, θ,Ψ) = 1 N1·N2
NX1−1 n1=0
NX2−1 n2=0
v(x, θ+ 2πn1,Ψ + 2πn2)−V(x). (9.2) The coherent fluctuations, resolved with respect to the acoustic forcing phase only, are defined as
vc,a(x,Ψ) = 1 2π
Z 2π 0
vc,ha(x, θ,Ψ)dθ. (9.3)
Analog to this, the coherent fluctuations, resolved with respect to the helical PVC phase only, are defined as
vc,h(x, θ) = 1 2π
Z 2π
0
vc,ha(x, θ,Ψ)dΨ. (9.4)
9.3 Experimental Observations
The results of the unforced and forced flow fields will be presented in the following for the three investigated combustor operating conditions.
0.5 2 3.5 5
−2 0 2
x/Dh;|U|/U0·1.5 y/Dh
(a) Isothermal flow
0.5 2 3.5 5 x/Dh;|U|/U0·1.5 (b) Attached V-flame
0.5 2 3.5 5 x/Dh;|U|/U0·1.5
0 0.5 1
U/U0
(c) Detached flame
Figure 9.2: Streamlines of the time-averaged flow fields without forcing are superimposed on the normalized axial velocity magnitude. At four axial locations, radial profiles of the normalized axial velocity are extracted. Dashed lines indicate zero axial velocity.
0.5 2 3.5 5
−2 0 2
x/Dh y/Dh
(a) Attached V-flame
0.5 2 3.5 5 x/Dh
0 0.5 1
IOH/IOH,max
(b) Detached flame
Figure 9.3: Streamlines of the unforced time-averaged flow field are superimposed on the normalized Abel-deconvoluted OH*-chemiluminescence intensity. Dashed lines indicate zero axial velocity.
9.3.1 Time-Averaged Flow Fields and Flow Field Dynamics without Acoustic Forcing
Figures 9.2 and 9.3 show the time-averaged flow fields encountered in the absence of acoustic forcing for the isothermal case, the detached flame, and the attached V-flame. The flow fields resemble very well the features observed in Chapter 4 for the different flame shapes.
Despite the higher velocities caused by the dilatation in the reacting case, the isothermal flow field and the flow field of the detached flame correspond well. The strong increase of the jet divergence is the most remarkable difference between the attached flame and the detached and isothermal case. In Chapter 4 it was shown for the same combustor geometry with a slightly larger centerbody that the isothermal flow field features a strong PVC. In the case of detached flames, the PVC remained very similar to the isothermal case, and in attached
9.3 Experimental Observations 153
0 0.2 0.4
Spectra
128.6 Hz
St mag(aj)
a1
a2 POD mode 1
0 2 4 6
−2 0 2
x/Dh y/Dh
POD mode 2
0 2 4 6
−2 0 2
x/Dh y/Dh
−1
−0.5 0 0.5 1
Ωxy/Ωxy,max
(a) Isothermal flow field
0 0.2 0.4
Spectra
St mag(aj)
a1
a2 POD mode 1
0 2 4 6
−2 0 2
x/Dh y/Dh
POD mode 2
0 2 4 6
−2 0 2
x/Dh y/Dh
−1
−0.5 0 0.5 1
Ωxy/Ωxy,max
(b) Attached V-flame
0 0.2 0.4
Spectra
135.3 Hz
St mag(aj)
a1
a2 POD mode 1
0 2 4 6
−2 0 2
x/Dh
y/Dh
POD mode 2
0 2 4 6
−2 0 2
x/Dh
y/Dh
−1
−0.5 0 0.5 1
Ωxy/Ωxy,max
(c) Detached flame
Figure 9.4: Results of the POD analysis of the isothermal flow, the detached flame, and the attached V-flame without acoustic forcing. Left column: Power spectra of the first two temporal POD coefficients. Middle and right columns: Normalized through-plane vorticity Ωxy of the first two spatial POD modes.
V-flame cases, it was completely suppressed. The same results are obtained from a POD analysis of the presently investigated unforced flow fields and are briefly presented here for the sake of completeness.
The two most energetic modes of the isothermal flow field in the absence of forcing, as can be seen in Fig 9.4a, show the same pattern of alternating vortices in the shear layers, as depicted in Fig. 4.6, and the spectra show a clear peak at a Strouhal number of St= 0.177,
corresponding to a frequency of 128.6 Hz. Hence, it is concluded that the isothermal flow field without forcing features a strong PVC. Its Strouhal number is considerably higher compared to the results presented in Chapter 4. This stems mostly from the definition of the Strouhal number, including the larger hydraulic diameter Dh and the lower combustor inlet bulk velocity U0 at the same mass flow rate.
For the attached V-flame case (Fig 9.4b), the POD analysis shows no signs of the PVC. The two most energetic modes indicate slow large-scale movements of the shear layers that are neither axisymmetric nor antisymmetric. In agreement with Chapter 4, the analysis suggests that in the V-flame case no PVC is present.
The results of the detached flame (Fig 9.4c) resemble very well the findings of Chapter 4.
The PVC is similar to the isothermal case in terms of frequency and spatial shape. Solely, the axial extend is slightly increased.
9.3.2 Time-Averaged Flow Fields with Acoustic Forcing
In Fig. 9.5 the time-averaged flow fields of the isothermal flow, the V-flame, and the detached flame are shown for forcing at a frequency of fa= 110 Hz and at forcing amplitudes ranging from |uc|/U0 = 0 to 1.25. Even though the focus of this chapter is placed on the flow field dynamics and the influence of acoustic forcing on the PVC, the time-averaged flow fields were identified as the determining factor for the self-excitation of the PVC (Chapter 4) and the amplification of the forced structures (Chapter 8). Thus, a close inspection of the time-averaged flow field is vital for the conclusions drawn in the remainder of this chapter.
The effect of forcing on the attached V-flame (Fig. 9.5b) is very similar to the cases presented in Chapter 8. The most striking effect of acoustic forcing on the flow field is a significant reduction of the width of the IRZ. The flame angle follows the opening angle of the jet and the flame is shifted upstream until the maximum heat release is located directly downstream of the centerbody. At high forcing amplitudes, the flow field and the flame shape show a remarkable similarity to the flow field of the trumpet flame in the unforced, steam-diluted case (compare Fig. 4.4b). Furthermore, the profiles of the normalized axial velocity clearly show that the backflow velocities close to the combustor inlet in the IRZ are significantly increased by the forcing.
The time-averaged isothermal flow field, as shown in Fig. 9.5a, is less affected by the acoustic forcing, than the flow field of the V-flame. The jet opening angle remains very similar even for very strong forcing. An increase of the back flow velocities can be observed in the axial velocity profiles, but it is much smaller compared to the attached V-flame. The influence of acoustic forcing on the flow field of the detached flame is comparable to the isothermal case.
The jet divergence remains constant and the backflow intensity is slightly increased. The heat release distribution of the detached flame is only weakly affected by the forcing.
9.3 Experimental Observations 155
0.5 2 3.5 5
−2 0 2
x/Dh;U/U0·1.5 y/Dh
(a) Isothermal
0.5 2 3.5 5 x/Dh;U/U0·1.5
0.5 2 3.5 5 x/Dh;U/U0·1.5
0.5 2 3.5 5 x/Dh;U/U0·1.5
0.5 2 3.5 5
−2 0 2
x/Dh;U/U0·1.5 y/Dh
0.2 0.4 0.6 0.8 IOH/IOH,max
(b) Attached V-flame
0.5 2 3.5 5 x/Dh;U/U0·1.5
0.2 0.4 0.6 0.8 IOH/IOH,max
0.5 2 3.5 5 x/Dh;U/U0·1.5
0.2 0.4 0.6 0.8 IOH/IOH,max
0.5 2 3.5 5 x/Dh;U/U0·1.5
0.2 0.4 0.6 0.8 IOH/IOH,max
0.5 2 3.5 5
−2 0 2
x/Dh;U/U0·1.5 y/Dh
0.2 0.4 0.6 0.8 IOH/IOH,max
(c) Detached flame
0.5 2 3.5 5 x/Dh;U/U0·1.5
0.2 0.4 0.6 0.8 IOH/IOH,max
0.5 2 3.5 5 x/Dh;U/U0·1.5
0.2 0.4 0.6 0.8 IOH/IOH,max
0.5 2 3.5 5 x/Dh;U/U0·1.5
0.2 0.4 0.6 0.8 IOH/IOH,max
Figure 9.5: Flow fields (a-c) and normalized Abel-deconvoluted OH*-chemiluminescence in-tensity distribution (b,c) of the encountered flow field and flame shapes at increasing forcing amplitudes. Forcing is increased from left to right from |uc|/U0 = 0 to |uc|/U0 ≈1.2 at a forcing frequency of fa = 110 Hz. The solid black lines are radial profiles of the normalized axial velocity and the dashed black lines represent isolines of zero axial velocity.
fa 2fa 3fa
0 0.5 1
0 100 200 300
|uc|/U0
f(Hz)
(a)fa= 110 Hz; symmetric spectra
fh fh+fa
fh−fa fh+ 2fa
0 0.5 1
0 100 200 300
|uc|/U0
f(Hz)
0.2 0.5 0.9
NormalizedPSD
(b)fa= 110 Hz; antisymmetric spectra
fa 2fa
0 0.5 1
0 100 200 300
|uc|/U0
f(Hz)
(c)fa= 158 Hz; symmetric spectra
fh fh+fa
fa−fh
0 0.5 1
0 100 200 300
|uc|/U0
f(Hz)
0.2 0.5 0.9
NormalizedPSD
(d)fa= 158 Hz; antisymmetric spectra
Figure 9.6: Spectra of the isothermal flow field dynamics at increasing forcing amplitudes.
Left: Symmetric spectra showing peaks at the forcing frequency. Right: Antisymmetric spectra.
9.3.3 Flow Field Dynamics with Acoustic Forcing
In the following, the flow field dynamics of the detached flame, the isothermal case, and the attached V-flame are analyzed at increasing forcing amplitudes and at two acoustic forcing frequencies. In order to obtain an overview of the frequency content in the flow field, the concept of symmetric and antisymmetric spectra, as described in Section 2.5, is employed.
The spectra are calculated for all measured spatial locations and are subsequently averaged to increase the signal-to-noise ratio.
Isothermal Flow Field
The results of the spectral analysis are provided for the isothermal case in Fig. 9.6. The left side shows the spectra of the symmetric velocity fluctuations, whereas the right side shows the spectra of the antisymmetric fluctuations. It can be observed that, in the absence of forcing (|uc|/U0 = 0), the only spectral peak can be found in the antisymmetric spectra at f ≈128.6 Hz. This frequency corresponds to a Strouhal number ofSt≈0.177 and is caused
9.3 Experimental Observations 157 by the PVC, depicted in Fig. 9.4a. At increasing acoustic forcing amplitude, the peak at the forcing frequency, and its harmonics, get more pronounced in the symmetric spectra. In the antisymmetric spectra, in contrast to this, only very weak traces of the forcing frequencies are visible, since the forced structures are essentially axisymmetric. The small contribution to the antisymmetric spectra is assumed to stem from the lack of perfect axisymmetry of the mean flow field, which are assumed to cause a deviation from perfect axisymmetry of the forced structures.
When the forcing frequency is higher than the frequency of the PVC (fa = 158 Hz, Fig. 9.6c,d), the effect of low amplitude acoustic forcing on the PVC is quite weak. The PVC is only slightly damped up to forcing amplitudes of |uc|/U0 = 0.6 and its frequency is slightly reduced. For higher forcing amplitudes, the damping of the PVC gets considerably stronger. Beside the peak corresponding to the PVC, two additional peaks can be clearly observed in the antisymmetric spectra for almost all forcing amplitudes. These peaks occur at the difference frequency of the forcing frequency and the PVC frequency (fa−fh) and at the sum of both frequencies (fh+fa).
In order to get a better insight into the flow dynamics, a POD analysis is carried out at a forcing amplitude of |uc|/U0 = 0.71 and a forcing frequency of fa = 158 Hz. Analog to the symmetric and antisymmetric spectra, the POD analysis is carried out first on the symmetric fluctuations and subsequently on the antisymmetric fluctuations. The results of the symmetric POD, depicted in the top row of Fig. 9.7, show two spatial modes describing the convection of the forced vortices in the shear layers. These forced structures are essentially the same structures that were observed in Chapter 8 and cause integral heat release fluctuations.
The spectra of the corresponding time coefficients reveal the forcing frequency and higher harmonics.
The antisymmetric POD at forced conditions (bottom row of Fig. 9.7) yields two modes describing the PVC. In comparison to the unforced case (Fig. 9.4a), the axial extent of the PVC is slightly reduced. The spectra of the two modes representing the PVC show the same peaks as the averaged antisymmetric spectra (Fig. 9.6) at the frequency of the PVC and at the sum and the difference of the forced frequency and the PVC frequency (fa−fh and fh+fa).
The dynamics of the flow field forced at fa = 110 Hz (Fig. 9.6a,b) show a qualitatively similar behavior as the flow field forced at fa = 158 Hz. However, the peak corresponding to the PVC dynamics only remains unaltered up to forcing amplitudes of |uc|/U0 = 0.3. At higher forcing amplitudes, the peak is notably damped and several peaks at the difference frequency of the PVC frequency and the forcing frequency (fh −fa) and at sums of both frequencies (fh+fa and fh+ 2fa) occur.
Since the spectral peak related to the PVC is strongly attenuated by the forcing, it is of interest how the spatial shape of the PVC is affected by the forcing. The evolution of the PVC is determined through the application of antisymmetric POD. At each forcing amplitude, it was visually checked that the two most energetic antisymmetric modes describe the same dynamic feature and correspond to the PVC. As it was described in Section 2.3, in this case
Spectra fa
2fa PSD(aj)
a1
a2 POD mode 1
−2 0 2 y/Dh
POD mode 2
−2 0 2 y/Dh
−1
−0.5 0 0.5 1
Ωxy/Ωxy,max
0 0.2 0.4 0.6 Spectra
fh
fa+fh fa−fh
St PSD(aj)
a1
a2 POD mode 1
0 2 4 6
−2 0 2
x/Dh y/Dh
POD mode 2
0 2 4 6
−2 0 2
x/Dh y/Dh
−1
−0.5 0 0.5 1
Ωxy/Ωxy,max
Figure 9.7: Results of the symmetric (top) and antisymmetric (bottom) POD analysis of the isothermal flow with forcing at fa = 158 Hz and |uc|/U0 = 0.71. Left column: Power spectra of the first two temporal POD coefficients. Middle and right columns: Normalized through-plane vorticity Ωxy of the first two spatial POD modes.
0 0.2 0.4 0.6
fh−fa
fh fh+fa fh+ 2fa
St PSD(aj)
0 0.5 1
|uc |/U0
|uc|/U0= 0.51
0 2 4 6
x/Dh
|uc|/U0 = 0.00
0 2 4 6
−2 0 2
x/Dh y/Dh
|uc|/U0 = 0.86
0 2 4 6
x/Dh
|uc|/U0 = 1.12
0 2 4 6
x/Dh
−1
−0.5 0 0.5 1
Ωxy/Ωxy,max
Figure 9.8: Results of the antisymmetric POD analysis of the isothermal flow with forcing at fa = 110 Hz and |uc|/U0 = 0 to 1.12. Top: spectra of the first time coefficient. Bottom:
normalized through-plane vorticity Ωxy of the antisymmetric structure described by the first two spatial POD modes. Phase is adjusted to increase the comparability between the forcing amplitudes.
9.3 Experimental Observations 159
fa 2fa 3fa
0 0.5 1
0 100 200 300
|uc|/U0
f(Hz)
(a)fa = 110 Hz; symmetric spectra
fh
0 0.5 1
0 100 200 300
|uc|/U0
f(Hz)
0.2 0.5 0.9
NormalizedPSD
(b)fa= 110 Hz; antisymmetric spectra
fa 2fa
0 0.5 1
0 100 200 300
|uc|/U0
f(Hz)
(c) fa= 158 Hz; symmetric spectra
fh
fa−fh fa+fh
0 0.5 1
0 100 200 300
|uc|/U0
f(Hz)
0.2 0.5 0.9
NormalizedPSD
(d)fa= 158 Hz; antisymmetric spectra
Figure 9.9: Spectral analysis of the detached flame. Left: Symmetric spectra showing peaks at the forcing frequency. Right: Antisymmetric spectra.
the PVC can be reconstructed by a linear superposition of the first two POD modes.
vc,h(x, θ) =<
q
a21+a22(Φ1(x) +iΦ2(x)) e−iθ
(9.5) The shape of the PVC at increasing forcing amplitudes is shown in Fig. 9.8. To increase the comparability of the spatial shape of the PVC, the phaseθ is adjusted in Fig. 9.8 to achieve a maximum correlation between the different forcing amplitudes. It is evident that the PVC changes its shape with increasing forcing amplitude but still remains similar. Simultaneously, the fluctuating energy content captured by the first two modes is reduced by approximately 40% (not shown). The spectra of the temporal coefficients of the first POD modes show very well the peaks at the PVC frequency and at the interaction frequencies, similar to the antisymmetric spectra showed in Fig. 9.6b.
Detached Flame
The results of the spectral analysis for the detached flame are presented in Fig. 9.9. Very similar to the isothermal case, the peak at the frequency of the PVC is damped by the acoustic forcing. However, it can be observed that the damping is considerably stronger for the reacting cases. Only for very low forcing amplitudes (|uc|/U0 < 0.25), the effect of the forcing is comparably low. For increasing forcing amplitudes the spectral peak corresponding to the PVC is strongly damped and finally gets completely suppressed. This suppression is considerably stronger for forcing at 110 Hz compared to 158 Hz forcing. The POD analysis of the fa= 158 Hz and|uc|/U0 = 0.5 case (Fig. 9.10) shows similar results as in the isothermal case. The forcing excites axisymmetric structures, but the two POD modes representing the PVC remain very similar to the unforced case (compare Fig. 9.4c).
The effect of forcing on the spatial shape of the PVC is investigated using antisymmetric POD, similar as it was done in the isothermal case. The results are presented in Fig. 9.11 for forcing atfa = 110 Hz. It is evident that the spatial shape of the PVC is significantly affected by the forcing. However, even at the highest forcing amplitude (|uc|/U0= 1.16), it still shows some similarity to the unforced case. This is particularly interesting, since already at forcing amplitudes |uc|/U0>0.4, no spectral peak of the PVC could be observed, whereas the POD still identifies similar coherent structures as in the unforced case. The explanation for this can be found considering the spectra corresponding to the POD modes describing the PVC.
The temporal coefficients do not describe an oscillation at a well-defined frequency anymore, whereas the spatial structure seems to persist in the forced flow field.
Attached V-Flame
The spectra of the attached V-flame (Fig. 9.12) show very different characteristics compared to the isothermal case and the detached flame case. In the absence of forcing, no self-excited antisymmetric structure is present, thus, no peak in the antisymmetric spectra is evident.
However, when the forcing amplitude, both at fa = 110 Hz and 158 Hz, reaches a certain value, the spectra of the antisymmetric fluctuations show distinct peaks at fh =50 Hz. An increase of the forcing amplitude leads to an increase of the frequency to almostfh= 100 Hz.
This frequency range is not related to the forcing frequency and gives rise to the assumption that the spectral peak is caused by a self-excited antisymmetric instability, such as the PVC.
Furthermore, also peaks at the difference of the acoustic frequency and the frequency of the self-excited structure are evident.
The POD analysis of the antisymmetric fluctuations (Fig 9.13) yields the dynamic feature that is related to the peak in the antisymmetric spectra. Similar to the unforced isothermal case and the unforced detached flame, the POD modes show a pattern of alternating vortices, and the second POD mode is shifted by a quarter wavelength relative to the first POD mode.
Compared to the isothermal and detached case, the POD modes describe a coherent structure that is considerably shifted downstream. When the POD modes are compared to the POD modes representing the PVC of the trumpet flame (Fig. 4.9), a reasonable similarity is evident.
This similarity is fully in line with the finding that the time-averaged flow field of the strongly
9.3 Experimental Observations 161
Spectra fa
2fa PSD(aj)
a1
a2 POD mode 1
−2 0 2 y/Dh
POD mode 2
−2 0 2 y/Dh
−1
−0.5 0 0.5 1
Ωxy/Ωxy,max
0 0.2 0.4 0.6 Spectra
fh
St PSD(aj)
a1
a2 POD mode 1
0 2 4 6
−2 0 2
x/Dh y/Dh
POD mode 2
0 2 4 6
−2 0 2
x/Dh y/Dh
−1
−0.5 0 0.5 1
Ωxy/Ωxy,max
Figure 9.10: Results of the symmetric (top) and antisymmetric (bottom) POD analysis of the detached flame with forcing at fa = 158 Hz and |uc|/U0 = 0.5. Left column: Power spectra of the first two temporal POD coefficients. Middle and right columns: Normalized through-plane vorticity Ωxy of the first two spatial POD modes.
0 0.2 0.4 0.6
fh
St PSD(aj)
0 0.5 1
|uc |/U0
|uc|/U0= 0.27
0 2 4 6
x/Dh
|uc|/U0 = 0.00
0 2 4 6
−2 0 2
x/Dh y/Dh
|uc|/U0 = 0.37
0 2 4 6
x/Dh
|uc|/U0 = 1.16
0 2 4 6
x/Dh
−1
−0.5 0 0.5 1
Ωxy/Ωxy,max
Figure 9.11: Results of the antisymmetric POD analysis of the detached flame with forcing at fa = 110 Hz and |uc|/U0 = 0 to 1.16. Top: spectra of the first time coefficient. Bottom:
normalized through-plane vorticity Ωxy of the antisymmetric structure described by the first two spatial POD modes. Phase is adjusted to increase the comparability between the forcing amplitudes.
fa 2fa 3fa
0 0.5 1
0 100 200 300
|uc|/U0
f(Hz)
(a)fa= 110 Hz; symmetric spectra
fh
0 0.5 1
0 100 200 300
|uc|/U0
f(Hz)
0.2 0.5 0.9
NormalizedPSD
(b)fa= 110 Hz; antisymmetric spectra
fa 2fa
0 0.5 1
0 100 200 300
|uc|/U0
f(Hz)
(c)fa= 158 Hz; symmetric spectra
fh fa−fh
0 0.5 1
0 100 200 300
|uc|/U0
f(Hz)
0.2 0.5 0.9
NormalizedPSD
(d)fa= 158 Hz; antisymmetric spectra
Figure 9.12: Spectral analysis of the attached V-flame. Left: Symmetric spectra showing peaks at the forcing frequency. Right: Antisymmetric spectra.
forced V-flame is similar to the time-averaged flow field of the trumpet flame. Thus, it seems very likely that the structure at fh = 50 to 100 Hz (depending on the forcing amplitude) is the PVC of the same type that occurs in the flow field of the trumpet flame. So far, the excitation of a PVC by axial acoustic forcing, in a case where no PVC is present without forcing, has not been reported in experiments and only in a numerical study by Giauque et al.
(2005).